\begin{abstract}
In Model-Driven Engineering, the potential advantages of using 
bidirectional transformations are largely recognized. Despite its 
crucial function, bidirectionality has somewhat limited success because of the 
ambivalence concerning non-bijectivity. In fact, consistently propagating 
changes from one side to the other is typically non univocal as more 
than one correct solution is admitted. This gives place to a form of \emph{uncertainty} which means that, rather than having a single model, we actually have a set of possible models but we do not know what is the desired one. In this paper, we discuss how dealing with multiple solutions is important and requires specialized tools and support. In particular, handling a set of models explicitly is generally impractical. Thus, we extended the semantics of the Janus Transformation Language to generate a model with uncertainty which is semantically equivalent to solution space.. The approach is implemented, a metamodel-independent construction is proposed, and operators for manipulating the uncertainty are also proposed.
\end{abstract}

